optimization - Finding multiple roots on an interval with Python -

-

i'm looking efficient method find roots of function f on interval [a,b]. problem have nice methods scipy.optimize require either f(a) , f(b) have different signs, or provide initial guess x0, know nothing roots before running code.

note: function f smooth (at least c1), , doesn't have pathological behaviour [nothing sin(1/x)]. however, requires building matrix a(x) , finding eigenvalues, , therefore time-consuming. expected have between 0 , 10 roots on [a,b], position arbitrary. can't afford missing of them (e.g. can't take 100 initial guesses x0 , hope i'll catch roots).

i thinking implementing this:

  1. find extrema {m_1, m_2.., m_k} of f scipy.optimize [maybe fmin, don't know method efficient]:
    • search minimum m_1 starting point [initial guess gradient algorithm]
    • search maximum m_2 starting point m_1 + dx [forcing gradient algorithm go forward]
    • search minimum m_3...
  2. if 2 consecutive extrema m_i , m_(i+1) have opposite signs, apply brentq on interval [m_i, m_(i+1)] find root.

  • is there better way of solving problem?

  • if not, fmin , brentq best choices among scipy.optimize library in order minimize number of calls function f?

one "usual" approach find approximant function, root finding easy, , find roots of approximant.

for instance, can sample function values @ number of points, fit spline points, , find roots of spline (which easy problem). @ least provide initial guesses roots.

the more tricky part determining sampling points. if know function c1, can sample more densely @ points function appears non-smooth, based on function values. needed years back, here's heuristic cooking approach problem way: https://gist.github.com/pv/acc71bafede0a84b074c7751985ecc6f worked me, ymmv.


Comments

Post a Comment

Popular posts from this blog

ios - RestKit 0.20 — CoreData: error: Failed to call designated initializer on NSManagedObject class (again) -

-
this error has shown on many times, seems. prominent answer issue seems restkit 0.20 — coredata: error: failed call designated initializer on nsmanagedobject class however, solution posted doesn't work me. let's start beginning: i want upload file server. want parse response make sure uploaded. if not, try again later. model has boolean variable called nsnumber *senttoserver purpose (in coredata, bool saved nsnumber ) . because don't know whether sending going successful, save entity coredata model first before sending via restkit. when post request successful, server returns json string this: {"id":14,"created":true} notice that, of course, id not set on coredata model yet, both id , created new informations model. here's model: @interface recording : nsmanagedobject @property (nonatomic, retain) nsstring * audiofilepath; @property (nonatomic, retain) nsdate * createdat; @property (nonatomic, retain) nsstring * deviceid; @
Read more

java - Digest auth with Spring Security using javaconfig -

-
so i'm trying create digest authentication spring following documentation trying translate xml "requirements" in java requirements. let's have xml in docs: <bean id="digestfilter" class= "org.springframework.security.web.authentication.www.digestauthenticationfilter"> <property name="userdetailsservice" ref="jdbcdaoimpl"/> <property name="authenticationentrypoint" ref="digestentrypoint"/> <property name="usercache" ref="usercache"/> </bean> <bean id="digestentrypoint" class= "org.springframework.security.web.authentication.www.digestauthenticationentrypoint"> <property name="realmname" value="contacts realm via digest authentication"/> <property name="key" value="acegi"/> <property name="noncevalidityseconds" value="10"/> </b
Read more

laravel - PDOException in Connector.php line 55: SQLSTATE[HY000] [1045] Access denied for user 'root'@'localhost' (using password: YES) -

-
my .env: app_env=local app_debug=true app_key=myappkey app_url=http://localhost db_connection=mysql db_host=localhost db_port=3306 db_database=gestiontaller db_username=root db_password='root' cache_driver=file session_driver=file queue_driver=sync redis_host=127.0.0.1 redis_password=null redis_port=6379 mail_driver=smtp mail_host=mailtrap.io mail_port=2525 mail_username=null mail_password=null mail_encryption=null i've tried password ", ' , without, restarting server every time. i've tried changing localhost 172.0.0.1. yes, password correct, running mysql -u root -p introducing password root in prompt can go mysql. users table: +------------------+-----------+ | user | host | +------------------+-----------+ | debian-sys-maint | localhost | | mysql.sys | localhost | | root | localhost | | root1 | localhost | +------------------+-----------+ i've added homestead.yaml this: database_port: 3306
Read more